Problem: Solve for $x$ and $y$ using substitution. ${6x-3y = -9}$ ${y = 3x+8}$
Explanation: Since $y$ has already been solved for, substitute $3x+8$ for $y$ in the first equation. ${6x - 3}{(3x+8)}{= -9}$ Simplify and solve for $x$ $6x-9x - 24 = -9$ $-3x-24 = -9$ $-3x-24{+24} = -9{+24}$ $-3x = 15$ $\dfrac{-3x}{{-3}} = \dfrac{15}{{-3}}$ ${x = -5}$ Now that you know ${x = -5}$ , plug it back into $\thinspace {y = 3x+8}\thinspace$ to find $y$ ${y = 3}{(-5)}{ + 8}$ $y = -15 + 8$ $y = -7$ You can also plug ${x = -5}$ into $\thinspace {6x-3y = -9}\thinspace$ and get the same answer for $y$ : ${6}{(-5)}{ - 3y = -9}$ ${y = -7}$